Mechanical Engg Thermodynamics

1. Chapter 7
Properties of Pure Substances
If any two independent intensive properties of a simple compressible system are defined,
other properties automatically assume definite values. These properties can be expressed in terms
of charts, tables or equations. This chapter covers the charts and tables of properties of steam.
7.1 Pure Substances
Substances of fixed chemical composition are known as pure substances
Example : Water, Helium, Nitrogen, Oxygen etc.
Substances exist in any one of the three phases namely solid, liquid and gas. For example,
H2O may exist in the form ice (solid), Water (Liquid) or Steam (Gaseous). In all these phases it
will have the same chemical composition.
A Mixture of two or more phases of a pure substance should also be regarded as pure
substance. If Water and Steam Co-exits in a container, the chemical composition of both the
Vapour and liquid phases will be identical. Hence this heterogeneous system is also a pure
substance.
7.2 Phase Transformation
Consider a unit mass of ice heated steadily at a constant pressure of 1 atm. Let the initial
temperature be -30oC. Due to heating, temperature increases upto 0oC (Figure 7.1). At 0oC ice
starts melting. Until entire mass of ice becomes water, temperature is remaining constant. Heat
added during this
phase change is
known as latent
heat of fusion.

2. Further heating increases the temperature of water. This continues until 100oC. At 100oC
Evaporation of water into steam is taking place. Temperature once again remains constant at
100oC until complete conversion of water into steam occurs. Heat added during this phase change
is known as latent heat of evaporation. Temperature of steam continues to increase afterwards.
7.3 p -T Diagram of a Pure Substance
Instead of 1atm. pressure, if water is heated at 5 bar, evaporation will be taking place at 15
1.86oC. In the similar manner, each pressure has its own saturation temperature for a given
substance.
In a p-T diagram the locus of saturation temperatures against the corresponding pressures
forms a curve known as vaporisation curve. It separates liquid and vapour phases is p-T diagram.
Similarly solid & liquid phases are separated by fusion curve in p-T diagram.
Below a limiting value of pressure known as Triple point, direct conversion of solid into
vapour is taking place. This is known as sublimation. Sublimation curve separate solid and
vapour phases in p-T diagram. Sublimation curve, vapourisation curve and fusion curve are
represented on a p-T Coordinates in Figure7.2. Sublimation and vapourisation curves are having
positives slopes for all substances. Fusion curve for most of the substances is having positive
slope but for water it is negative. From p-T diagram it can be inferred that the given substance
exists in liquid phase when the temperature is below the saturation temperature corresponding to
the given pressure and in vapour phase if the given temperature is greater than the saturation
temperature. When the given temperature is equal to the saturation temperature it may be liquid,
vapor (or) a mixture of both.

3. 7.4 T-v Diagram of a Pure Substance
For simplicity let us consider only the liquid and vapour phases, which are commonly
encountered in most of the engineering applications. Let a system of unit mass of water be heated
at constant pressure. 1-2-3-4 in Figure 7.3 Shows the T-v Variations at constant pressure.
From 1 to 2, heat addition increases the temperature with a very small increase in volume.
State of water between 1 to 2 is known as subcooled liquid or compressed liquid because for a
given pressure it is at a temperature lower than the saturation temperature (or) for a given
temperature it is at a pressure higher than saturation pressure. The state of water at 2 is known
saturated liquid. Temperature at this state is equal to the saturation temperature. Any further
addition of heat causes evaporation of water.
From 2-3 evaporation is taking place. During this phase change, temperature remains
constant and increase in volume is high. At state 3, entire mass is in the form of vapour known
dry saturated vapour.
From 3 to 4, heating causes increase in both temperature and volume. State of steam in this
region is called super heated state.
As mentioned earlier, at higher pressure evaporation occurs at higher temperature and at
lower pressure evaporation occurs at lower temperature. Latent heat of evaporation decreases
with increase in pressure. For a particular pressure it becomes zero so that the change from liquid
to vapour phase occurs suddenly without a distinct intermediate state. This pressure is known as
critical pressure. This state on a property diagram is known as critical point. By connecting the
saturated liquid state at different pressures a line called saturated liquid line is obtained. In the
same way, by connecting the saturated vapour states, saturated vapour line is obtained. It can be
observed that the saturated liquid and vapour line meet at critical point. Figure 7.4. Shows all
these lines and various regions on a T-v diagram.

4. The region between saturated liquid line and saturated vapour line is known as wet region,
consisting of both liquid and vapour. The percentage of composition or quality of this wet steam
is expressed in terms of dryness fraction which is defined as the ratio of mass of vapour to the
mass of the mixture. Specific volume of wet steam is expressed as
v = xvg + (1 - x)vf
= vf + x(vg - vf)
= vf + xvfg ...(7.1)
Where vf - specific volume of the saturate liquid @ the given Pressure or Temperature
vg - specific volume of sat. vapour @ the given Pressure or Temperature
x - dryness fraction.
Since vf<<vg
v = vf + xvg ...(7.2)
In the compressed liquid region, specific volume may be regarded as a function of temperature
alone since the liquid is incompressible.
v @ vf @ the given temperature.
In the superheated region, v is function of both temperature and pressure.
7.5 T-s Diagram for a Pure Substance
Similar to T-v diagram, T-s diagram can also be drawn for a pure substance. Figure 7.5
shows various regions on a T-s diagram. The salient features of this diagram are :
 Temperature is taken on Y-axis and entropy is taken on X-axis

5.  There are three distinct regions : to the left of the saturated liquid line is the liquid
region, between saturated liquid and saturated vapour line is wet region, and to the right
of saturated vapour line is superheated region
 Constant pressure lines coincide with the constant temperature lines in the wet region.
These lines becomes curved in the superheated region
 Slope of the saturated liquid line is less compared to that in T-v diagram.
Entropy of a fluid at saturated liquid state s = sf @ the given p or T
For saturated vapour state
s = sg @ the given p, T
For Wet state
s = sf + x sfg ...(7.3)
where sf and sfg are functions of p or T.
For superheated state
s = s(p, t)
For subcooled liquid
s = sf - cpl ln ...(7.4)
Where sf ® sat. liquid entropy @ the given pressure

6. cpl ® Liquid specific heat at the given temperature
Ts ® Sat. temp. corresponding to the given pressure
T ® Given Temperature.
7.6 h-s Diagram for a Pure Substance
Within the wet region both isobars and isotherms are the same, but beyond saturated
vapour line they deviate. Also it can be noted that the constant pressure lines diverge from each
other towards the super heated vapour region. In the super heated vapour region, slope of
isotherms become almost zero. The slope of constant pressure curves at any point is a measure of
temperature, by noting that .
7.7 p-v. Diagram Of A Pure Substance

7. Figure 7.7 shows the pv diagram of a pure substance. The saturated liquid and saturated-vapour
curves meet at the critical point. The region to the left of the saturated-liquid line is
compressed liquid, and the region to the right of the saturated-vapour line is superheated vapour.
In between the two lines is the two-phase liquid-vapour region. Several isotherms are shown in
the figure. The critical isotherm has an inflection point and a zero slope at the critical point.
Isotherms below the critical point experience two discontinuities in slope as they cross the
saturated-liquid and saturated-vapour lines. In between these two lines, the slope of the isotherms
is zero, and a state in this region can be entirely saturated liquid, entirely saturated vapour, or a
combination of the two.
7.8 Extending p-v Diagram for a Pure Substance to Solid Phase

9. Figure 7.8a. shows various regions of a pure substances on a p-v coordinates. Volume
continuously increases from solid to super heated vapour region. But for water volume decreases
on melting and afterwards increases as shown Figure 7.8b.
7.9 p-V-T Surface
p-V-T behaviour of a pure substance can be expressed in a single three dimensional p-v-t
surface as shown in the Figure 7.9(a). For water as its volume decreases on melting unlike other
substances its p-v-t surface will be different from that of others as given in Figure 7.9(b).

10. 7.10 Measurements of
Dryness Fraction of Wet Steam
Dryness fraction of wet steam, representing the fraction of steam in the mixture of water
and steam can be measured by using (i) Throttling calorimeter and (ii) Separating and Throttling
calorimeter. Principle and working of these two devices are presented in this section.
(i) Throttling calorimeter
Let us consider a wet steam as represented by state 1 in the h-s diagram as given in Figure
7.10. When it undergoes a throttling process to state 2, it enters into the superheated region. By
measuring the temperature and pressure after throttling the specific enthalpy can be obtained. As
mentioned earlier during throttling enthalpy remains constant. Therefore the initial state can be
completely fixed since the pressure before throttling and the corresponding specific enthalpy are
known. That is,
h1 = hf1 + x1 hfg1 = h2
...(7.5)
where h2 = f (t2, p2)
hf1 = hf@p1
hfg1 = hfg@p1 .

11. Schematic arrangement of a throttling calorimeter is given in Figure 7.11. Steam from the
main is extracted through a perforated tube projecting into it as shown in the Figure. Pressure of
the steam is measured. It is then throttled into a chamber where the necessary pressure and
temperature measurements are made. From the chamber the expanded steam is then condensed by
circulating cooling water and discharged.

12. (ii) Separating and Throttling calorimeter
When the dryness fraction of the steam is very low, it becomes superheated vapour only at
very low end pressure on throttling. In general, the pressure after throttling for dryness fraction
measurement is preferred to be above atmospheric. In such applications, separating and throttling
calorimeters are used for dryness fraction measurement.
Wet steam, when subjected to sudden change in the direction of flow, a portion of the
liquid falls due to gravity and gets separated from the main stream. Thus the remaining steam
becomes rich in vapour, which upon throttling will become superheated vapour even at a pressure
higher than atmospheric pressure. This principle is employed in the separating and throttling
calorimeter.
The schematic arrangement of a separating and throttling calorimeter is shown in Figure
7.13. The wet steam from the steam main is extracted through a perforated tube and sent to the
separator where a portion of the liquid is separated due to sudden change in the direction as
explained above. The remaining steam is throttled into a chamber where the required pressure and
temperature measurements are made. Mass flow rate of liquid separated in the separator is
collected and measured. Mass of the remaining steam is also measured by condensing the
throttled steam and collecting it. Let be the mass of liquid separated in the separator and be the
mass of steam throttled. The state of steam before entering the separator is denoted as state1 and
states before and after throttling are respectively represented as state 2 and state 3.

13. As throttling is a constant enthalpy process
h2 = h3
...(7.6)
where h3 = f(T3, p3) ; Since pressure and temperature after throttling are known,
from the superheated steam table, h3 can be obtained.
These two values can be obtained from the saturated table
Therefore x2 can be computed from equation (7.6 ).

14. It has already been mentioned that only liquid is being separated from the wet steam when
it is passed through the separator. Then the mass of dry vapour leaving the separator must be
equal to the mass of dry vapour entering the separator.
That is
(m1 + m2) x1 = m2 x2
Upon rearranging the equation
...(7.7)
7.11 Steam Tables
As defined earlier to define the thermodynamic state of a given substance, any two
independent intensive properties are sufficient. Once the state is fixed, all other properties can be
computed. Tables giving the property values of saturated liquid and saturated vapour with respect
temperature and pressure are available along with the properties of superheated steam. These
tables can be made use of in the calculation of properties at any state. [See Appendix A1 & A2]
For refrigeration application, fluids like Ammonia and R134a are used. Properties of these
fluids are also available in the form of tables.